A solid sphere just fits inside a cube that has an
edge length equal to the diameter of the sphere.
The edge length of the cube is 5.8 cm. What is
the volume of air in the cube to the nearest
cubic centimetre?
93 cm cubed
v^3 = 5.8^3
vsphere = (4/3) pi (5.3/2)^3
subtract
12
How did you get 5.3/2 in the volume of a sphere
To find the volume of air in the cube, we first need to calculate the volume of the sphere that fits inside it.
Since the edge length of the cube is equal to the diameter of the sphere, we can conclude that the diameter of the sphere is also 5.8 cm.
To find the volume of the sphere, we can use the formula:
Volume = (4/3) * π * radius^3
Since the diameter of the sphere is 5.8 cm, the radius would be half of that, which is 2.9 cm.
Now we can substitute the values into the formula:
Volume = (4/3) * π * 2.9^3
Calculating this, we get:
Volume ≈ 4.19 * 24.389
Volume ≈ 101.786 cubic centimeters
So the volume of the sphere is approximately 101.786 cubic centimeters.
To find the volume of air in the cube, we subtract the volume of the sphere from the volume of the cube.
The formula to calculate the volume of a cube is:
Volume = edge length^3
In this case, the edge length is 5.8 cm.
Calculating the volume of the cube:
Volume = 5.8^3
Volume ≈ 5.8 * 5.8 * 5.8
Volume ≈ 195.1128 cubic centimeters
Now, subtract the volume of the sphere from the volume of the cube:
Volume of air = Volume of cube - Volume of sphere
Volume of air ≈ 195.1128 - 101.786
Volume of air ≈ 93.3268 cubic centimeters
Therefore, the volume of air in the cube to the nearest cubic centimeter is approximately 93 cubic centimeters.